Advertisement

(Given: The value of the universal gravitational constant is 6.672e−11 N · m2/kg2)

Objects with masses of 224 kg and 614 kg are separated by 0.369 m. A 61.1 kg mass is placed midway between them.

a) Find the magnitude of the net gravitational force exerted by the two larger masses on the 61.1 kg mass. Answer in units of N

b) Leaving the distance between the 224 kg and the 614 kg masses fixed, at what distance from the 614 kg mass (other than infinitely remote ones) does the 61.1 kg mass experience a net

force of zero? Answer in units of m

The gravitational force between two bodies is given by:

Fg=G*m1*m2/R^2

In this case the gravitational force of the left mass m1 on the center mass m3 will be:

Fg13=G*m1*m3/R13^2=(6.67x10^-11)*224*61.1/(.369/2)^2=2.68x10^-5N left

While the gravitational force on the center mass by the right mass will be:

Fg23=G*m2*m3/R23^2=2=(6.67x10^-11)*614*61.1/(.369/2)^2=7.35x10^-5 right

Since force is a vector subtract to determine the net force,on th center mass

Fgnet=Fg23-Fg13=4.67x10^-5N right

For the center mass to feel zero net force these two gravitational forces must be equal:

Fg13=Fg23

G*m1*m3/R13^2=G*m2*m3/R3023^2

Simplifying:

m1/R13^2=m2/R23^2

Solve for R23 in terms of R13:

m2/m1=R23^2/R13^2

R23=R13*sqrt(m2/m1)=R13*sqrt(614/224)=1.66*R13

Since these two distance must add up to 0.369m:

R13+R23=R13+1.66*R13=2.66*R13=0.369

Therefore, R13 becomes:

R13=0.369/1.66=0.139m

And:

R23=0.369-R13=0.369-0.139=0.230m

Physics

Answers by Expert:

I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.